7 people can paint 6 walls in 34 minutes. How many minutes will it take for 9 people to paint 8 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 7\text{ people}\\ t &= 34\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{34 \cdot 7} = \dfrac{3}{119}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{3}{119} \cdot 9} = \dfrac{8}{\dfrac{27}{119}} = \dfrac{952}{27}\text{ minutes}$ $= 35 \dfrac{7}{27}\text{ minutes}$ Round to the nearest minute: $t = 35\text{ minutes}$